Trajectory tracking control for ships with fixed-time prescribed performance considering input saturation and dead zone

To enable underactuated ships to achieve trajectory tracking under unknown external disturbances, model uncertainties, and actuator saturation and dead zone, a fixed-time prescribed performance trajectory tracking control method is designed. Firstly, the position tracking errors are constrained by designing the barrier Lyapunov function, and the prescribed performance function is set as the constraint boundary to address the issue of fixed constraint boundaries in traditional methods. Secondly, RBF neural networks are employed to estimate the model uncertainties, and adaptive laws are used to estimate the upper bound of the composite disturbances. Finally, the controller is designed by incorporating fixed-time convergence theory and further using fixed-time sliding mode surface in order to overcome the shortcomings of traditional control algorithms in terms of slow response and the use of finite-time convergence with respect to the initial state. Through Lyapunov stability analysis, it is proven that all signals in the closed-loop system are bounded, and the velocity tracking errors can achieve global fixed-time convergence. Simulation results demonstrate that the proposed control scheme enables underactuated ship to achieve trajectory tracking even in the presence of input saturation and dead zone. Statistical results show that the performance indicators of the proposed controller are significantly smaller than those of the first group in the comparative experiments, with a shorter settling time. Moreover, compared to traditional saturation handling methods, the input curves of the proposed controller are smoother and more aligned with practical engineering requirements.